This is an open access article published under an ACS AuthorChoice License, which permits copying and redistribution of the article or any adaptations for non-commercial purposes.
Research Article Cite This: ACS Cent. Sci. XXXX, XXX, XXX−XXX
http://pubs.acs.org/journal/acscii
Tuning the Electric Field Response of MOFs by Rotatable Dipolar Linkers Johannes P. Dürholt, Babak Farhadi Jahromi, and Rochus Schmid* Computational Materials Chemistry Group, Fakultät für Chemie und Biochemie, Ruhr-Universität Bochum, Bochum 44801, Germany
Downloaded via 185.46.86.226 on August 27, 2019 at 14:15:33 (UTC). See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles.
S Supporting Information *
ABSTRACT: Recently the possibility of using electric fields as a further stimulus to trigger structural changes in metal−organic frameworks (MOFs) has been investigated. In general, rotatable groups or other types of mechanical motion can be driven by electric fields. In this study we demonstrate how the electric response of MOFs can be tuned by adding rotatable dipolar linkers, generating a material that exhibits paraelectric behavior in two dimensions and dielectric behavior in one dimension. The suitability of four different methods to compute the relative permittivity κ by means of molecular dynamics simulations was validated. The dependency of the permittivity on temperature T and dipole strength μ was determined. It was found that the herein investigated systems exhibit a high degree of tunability and substantially larger dielectric constants as expected for MOFs in general. The temperature dependency of κ obeys the Curie−Weiss law. In addition, the influence of dipolar linkers on the electric field induced breathing behavior was investigated. With increasing dipole moment, lower field strengths are required to trigger the contraction. These investigations set the stage for an application of such systems as dielectric sensors, order−disorder ferroelectrics, or any scenario where movable dipolar fragments respond to external electric fields.
■
INTRODUCTION
On the other hand, in addition to guest adsorption, the regularity and porosity of MOFs make them an ideal platform to realize molecular machines. The void space allows for the motion of either the MOF building blocks, such as rotating linkers,16 or molecular guests inside the pores. For example, Loeb and co-workers incorporated a rotaxane moiety in the linker of an MOF.17 Very recently, the unidirectional rotation of a light-driven rotor within an MOF was demonstrated.18 Again, external electric fields are a facile way to trigger motion of movable components in MOFs. For example, Yazaydin and co-workers investigated two interesting systems in silico, where the transport of guests is modulated by the help of dipolar groups ordering in an external electric field. In the first case, a large dipolar molecule was mounted on the open metal coordination sites in Mg-MOF-74, which acts as a molecular gate, controlling the flow of guest molecules along the hexagonal channels.19 In the second example, the guest diffusion in an IRMOF variant with a dipolar group at the linker was modulated by applying an external field.20 Due to the ordering of linkers in the field, a nonisotropic self-diffusion was observed. To gain a deeper understanding of any kind of field induced motion or structural transformation in a system, its dielectric permittivity κ needs to be known. However, due to the general interest in electrically insulating MOFs as potential low-κ
Metal−organic frameworks (MOFs) are an emerging class of crystalline, hybrid, and porous materials, which are built from oligotopic molecules (linkers) and metal ion nodes.1−3 Potential applications for MOFs are gas separation and storage, water purification, chemical sensing, catalysis, drug delivery, and imaging.4−8 In particular, so-called stimuliresponsive MOFs, which undergo physical or chemical “changes of large amplitude in response to external stimulation”,9 have gained much attention for the design of new functional materials.10,11 Well-studied external stimuli are temperature, mechanical pressure, guest adsorption or evacuation, and light absorption. Recently, the possibility to use external electric fields E as a further stimulus to trigger structural changes in MOFs has been reported. By molecular dynamics simulations, the wellknown breathing behavior of MIL-53(Cr) could be reproduced, however, only by applying a very high external electric field.12 One of us proposed a potential mechanism for this transformation, based on field-induced dipole−dipole interactions in a wine-rack-type lattice (see Figure 6).13 Recently, Kolesnikov and co-workers confirmed this mechanism for a 2D lattice model by statistical mechanics calculations.14 Furthermore, Knebel et al. demonstrated that an electric field can be used to enhance the molecular sieving capability of a ZIF-8based MOF-polymer membrane by initiating reversible phase transitions.15 © XXXX American Chemical Society
Received: May 20, 2019
A
DOI: 10.1021/acscentsci.9b00497 ACS Cent. Sci. XXXX, XXX, XXX−XXX
Research Article
ACS Central Science
Figure 1. Investigated systems with zinc paddle-wheels as inorganic building blocks, which are connected in the pcu topology by phenyl moieties (blue) in the x- and y-direction and pillared in the z-direction by bispyridine units (red). Between the two pyridine units, different organic moieties (A−C) can be mounted to vary the dipole moment of the pillar linker.
keeping its other properties unaffected. Furthermore, this system is realistic and could even be deposited as a thin film on a device by layer-by-layer synthesis.29 For the determination of κ we followed the work by Zhang and Sprik who proposed four different methods to calculate κ from classical MD simulations in the case of liquid water (namely, from polarization fluctuations or as a finite field derivative with either fixed electric field E or fixed displacement charge field D).30 In contrast to the molecular liquid water, the herein investigated systems are porous crystalline polymers and show a nonisotropic dielectric response, since the dipolar linkers can only rotate around the z-axis. Furthermore, the dipole density is much lower and thus also the possible polarization. To determine the numerically most efficient way of predicting κ for such systems, the four proposed methods were applied to systems B and C, and its performance was validated. In addition, we verified the hypothesis that dipolar groups facilitate the electric field induced breathing13 which was observed originally for MIL-53.
interlayer dielectrics for semiconducting devices, past theoretical investigations were mainly focusing on the electronic polarization of rigid MOFs in the linear response regime. Note that a somewhat related current development is, on the other hand, electrically conducting MOFs, which respond by a current on an electric field.21 Nevertheless, in the context of MOFs as low-κ materials at first Zagorodniy et al. studied the dielectric response of cubic Zn-based frameworks, employing the semiempirical Clausius−Mossotti model.22 Later, Warmbier et al. employed density functional perturbation theory to calculate κ for similar rigid cubic frameworks.23 Inspired by these theoretical studies, the dielectric and optical properties of HKUST-124 and ZIF-825 were investigated experimentally, confirming that MOFs are indeed promising candidates for low-κ dielectrics.26 Recent theoretical investigations by Ryder and co-workers, again based on static density functional theory (DFT) calculations, established structure−property relations for the dielectric response of MOFs.27,28 They found only a minor dependency of κ on the chemical composition of the MOF but an almost linear dependency on the porosity. The dielectric properties of MOFs with incorporated dipolar rotors have, on the other hand, not been investigated up to now. In contrast to the systems studied by Ryder et al., a strong dependency of κ on the chemical composition, and in particular on the dipole strength of the rotor, is expected, since the highly temperature-dependent orientation polarization should dominate over the electronic polarization in these systems. As a consequence, molecular dynamics (MD) simulations at finite temperature are needed for the determination of the static dielectric permittivity κ. In this work we used pillared layer MOFs as reference systems to establish the methodology, and to investigate the influence of increasing dipole strength and temperature on the dielectric constant for a given framework structure. In our reference systems, square lattices of 1,4-benzenedicarboxylate (bdc) linked zinc paddle-wheels are pillared by bispyridine linkers as shown in Figure 1. The parent system (A) with a central phenyl exhibits no dipolar group. In B 1,2-difluorophenyl and in C phtalazine replace the phenyl in the backbone with an increasing dipole strength. This setup allows for an easy manipulation of the dielectric response of the material, by
■
METHODS Dielectric Constants from MD Simulations. When a material is exposed to an electric field, it becomes polarized. The induced polarization P is related to the electric field E by the electric susceptibility χ P = ϵ0χE
(1)
The relative permittivity of a material (i.e., its dielectric constant) κ is then given by κ = 1 + χ. In general, this relative permittivity is not a constant but depends on the frequency of the applied field, the temperature T, and other parameters. The induced polarization can be divided into three different contributions: electronic Pel, displacive (ionic) Pion, and orientation polarization Porient. Consequently, the relative permittivity can be written as κ = 1 + χel + χion + χorient. Pel corresponds to the response of the electron density to the electric field. At the high-frequency limit this contribution is crucial, since the nuclei move too slowly to adapt. The ionic polarization is due to the adaptation of the nuclei positions with respect to the electric field. Orientation polarization arises whenever molecules or molecular groups carry a permanent B
DOI: 10.1021/acscentsci.9b00497 ACS Cent. Sci. XXXX, XXX, XXX−XXX
Research Article
ACS Central Science dipole moment μ, which becomes partially aligned to the electric field. For polar liquids this third contribution becomes dominating. In their investigation on liquid water, Zhang and Sprik proposed four different methods to calculate relative permittivities from classical molecular dynamics simulations, based on two different Hamiltonians.30 In the constant-E method, the electric enthalpy - of a system of volume Ω is written as -(E , v) = HPBC(v) − ΩE ·P(v)
κx =
κx = 1 +
(2)
Ω [D − P(v)]2 2ϵ0
κx =
(5)
⟨Px⟩ ϵ 0E
(6)
1 1 − ⟨Px⟩/D
(7)
where the expectation value of the polarization is determined from an average over a trajectory generated by the constant Dx = D Hamiltonian. Note that, for both approaches, ⟨Px⟩ is obtained in relation to the average polarization from a trajectory at E = 0, with the same choice for the unit cell. Computational Details. All molecular dynamics simulations were performed using the MOF-FF force-field33,34 (parameter sets are provided in the SI), employing our inhouse developed PYDLPOLY code.33 The Ewald summation method was used for calculating the electrostatic interactions, and the short-range interactions were truncated smoothly at 12 Å. The unit cells for the materials were chosen as shown in Figure 6 by a rotation of 45° around the crystallographic c-axis of the conventional cell, which results in a unit cell 2 times larger than the conventional one. Simulations in the (N, V, T) ensemble for the calculations of the dielectric constants were performed in a 2 × 2 × 2 supercell of the rotated unit cell at temperatures of 150, 298, and 450 K. For every system and applied field strength the material was first equilibrated for 100 ps using a Berendsen thermostat35 with a time constant of 200 fs and then further simulated for at least 10 ns using a Nosé− Hoover thermostat36 with a time constant of 1 ps. For all simulations a time step of 1 fs was used. The polarization was monitored every 10th time step. Statistical errors of the polarization P were calculated by performing a reblocking analysis.37 For the investigation of the electric field induced breathing behavior, we always employed a larger 6 × 2 × 2 supercell of the rotated unit cell at 298 K and a pressure of 1 bar. At every field strength the system was first equilibrated for 50 ps in the (N, V, T) ensemble using a Berendsen thermostat35 with a time constant of 200 fs. Then, it was equilibrated in the (N, σ, T) ensemble for 2 ns by a Berendsen thermostat (time constant of 200 fs) and barostat (time constant of 1 ps) followed by a sampling run of 5 ns using a Nosé−Hoover thermostat (time constant of 1 ps) and barostat (time constant of 1 ps).
(3)
0
to MD simulations using the fixed-E approach, here, the instantaneous polarization P has to be known at every time step, because the force depends explicitly on its value. Since P is a multivalued property and depends on the choice of the unit cell,32 it has to be assured that all atoms are kept in the same reference frame during the simulation. Furthermore, because MOFs are crystalline periodic materials, it is practically impossible to define a unit cell with a vanishing dipole moment and thus a polarization of zero. Therefore, prerequisite to a simulation with a fixed-D Hamiltonian, a corresponding simulation with E = 0 has to be performed to sample the polarization at zero field for the unit cell of choice, which is then used as reference polarization in eq 3. In general, as discussed already by Stengel et al., the constant-E Hamiltonian corresponds macroscopically to a capacitor in short circuit, since polarization fluctuations have to be compensated by fluctuating charges on the capacitor plates. In contrast, the constant-D Hamiltonian is related to a capacitor in open-circuit conditions with a fixed value of free charge Q on the plates, with the polarization fluctuations leading to a fluctuating field E.30,31 Relative permittivities κ can now be derived from polarization fluctuations at either E = 0 (using the fixed-E Hamiltonian from eq 2) or D = 0 (using the fixed-D Hamiltonian from eq 3). With E = 0, κ can be derived from the fluctuations of the polarization P by Ω (⟨Px2⟩E = 0 − ⟨Px⟩2E = 0 ) ϵ0kBT
− ⟨Px⟩2D = 0 )
with ⟨Px⟩ the expectation value of the polarization obtained from an MD run using the constant Ex = E Hamiltonian. The finite D derived value for κ follows from the relation
where D denotes the fixed macroscopic electric displacement field and ϵ0 the vacuum permittivity.31 From this follows that q the field-dependent force on atom i is ϵ i (D − P). In contrast
κx = 1 +
1−
Furthermore, relative permittivities can also be estimated from simulations for a finite field by extrapolating then to the limit of zero field. For an electric field E, κ can be computed by using the relation
where HPBC is a classical Hamiltonian with v denoting the set of momenta and positions of the atoms, E is the fixed electric field, and P(v) is the macroscopic polarization for the microscopic state specified by v. Note that the SI unit system is used in this work throughout (conversion formulas to the CGS unit system are given in the SI). Thus, the fielddependent force on atom i is qiE, where qi is the charge assigned to the atom in the FF model. In the constant-D method, the electric internal energy
